President Donald Trump is considering turning his focus away from a heated Republican primary runoff in Alabama, according to multiple Republicans close to the White House, potentially underscoring the deteriorating relationship between the president and the Senate GOP.

Trump's initial endorsement of Sen. Luther Strange, R-Ala., aligned him with Senate Majority Leader Mitch McConnell, R-Ky., and his allies, who plan to invest millions of dollars trying to nudge Strange past controversial former judge Roy Moore. Strange, who was appointed to the seat formerly held by Attorney General Jeff Sessions, placed second behind Moore in the first round of voting earlier this month and has struggled to excite Alabama's conservative, pro-Trump base.

Trump did not signal a desire this week to formally withdraw his endorsement of Strange, the Republicans said, speaking on the condition of anonymity to describe private conversations. And with the president having proven to be unpredictable, the individuals offered no certainty that he would stay out of the runoff.

But Trump is considering being less engaged than in the first round of voting, when he tweeted his support and recorded a robo-call for the senator, they said - potentially turning the contest into yet another example of the frayed relationship between Trump and McConnell.

The Republicans added that the calculus being made in Trump's orbit is logical. With a bevy of challenges on Capitol Hill this fall, the president is unlikely to have much time or political capital to spend on Strange's campaign. On Friday, Trump and Vice President Mike Pence called Strange to assure him of their support but made no specific plans to campaign on his behalf, according to two individuals with knowledge of the call.

Brynn Anderson / AP

Former Alabama Chief Justice and U.S. Senate candidate Roy Moore speaks to supporters, Tuesday, Aug. 15, 2017, in Montgomery, Ala. Moore, who took losing stands for the public display of the Ten Commandments and against gay marriage, forced a Senate primary runoff with Sen. Luther Strange, an appointed incumbent backed by both President Donald Trump and heavy investment from establishment Republican forces.

Former Alabama Chief Justice and U.S. Senate candidate Roy Moore speaks to supporters, Tuesday, Aug. 15, 2017, in Montgomery, Ala. Moore, who took losing stands for the public display of the Ten Commandments and against gay marriage, forced a Senate primary runoff with Sen. Luther Strange, an appointed incumbent backed by both President Donald Trump and heavy investment from establishment Republican forces.

(Brynn Anderson / AP)

The dynamic also places the spotlight on Moore, an insurgent conservative best known for having been pulled from office after defying a 2003 court order to remove a monument to the Ten Commandments from the courthouse where he served as the state's chief justice. Moore was elected chief justice a second time - but was again removed, in 2016, after refusing to comply with a U.S. Supreme Court decision legalizing same-sex marriage.

Moore, along with Trump, remains popular among Alabama Republicans. Moore and Strange earned 39 percent and 33 percent, respectively, in the first round of voting. And while Strange has embraced Trump at every turn during the campaign, private polling this week from a pro-Strange group shows him narrowly trailing Moore in the runoff. For both McConnell and Trump - for the GOP establishment and its insurgent wing - the stakes will be high during the next four weeks.

With Strange in the Senate, McConnell's job would be easier than with Moore, a far-right fire thrower who sent a fundraising email this week with the subject line, "It's time to take King McConnell's crown." A Moore win also would raise the possibility that future Republican Senate candidates would run on an anti-McConnell promise, especially in red-state primary races - putting his leadership in jeopardy.

For Trump, who has built a brand on winning, a Strange loss in Alabama could tarnish his image as a titan of the Republican base and raise questions about how much sway he holds in down-ballot contests heading into the midterm elections.

In some ways, Moore, who has engaged in the false "birther" conspiracy about President Barack Obama and is no stranger to controversy, resembles Trump. But Strange has built a relationship with the president and could urge him to act on his behalf.

Inside the West Wing, advisers have urged the president to target GOP leaders - and to not weigh in as much, if at all, for Strange. There are no plans yet for Trump to travel to Alabama to rally with Strange, although the discussions are fluid, the Republicans close to the White House said. They spoke on the condition of anonymity to describe internal deliberations.

Trump has built a rapport over the phone with Strange on several occasions. But people familiar with the relationship said that it is more friendly than politically intertwined, and that Trump does not feel compelled to do more than he already has.

While Trump has not personally soured on Strange, the Republicans said he is well aware of the senator's fall in the polls and is more focused on the barrage of legislative battles he faces on Capitol Hill.

The White House press office did not immediately respond to a request for comment.

Republicans close to Strange still hope the president will wade in again ahead of the Sept. 26 vote. Several said that Trump would need to do more than the two tweets and robo-call that helped boost Strange into the two-person runoff.

Trump crushed the competition in Alabama in the 2016 Republican primary and coasted to victory in the state over Hillary Clinton in the general election.

"He clearly packs a wallop," said Steven Law, the president and chief executive of the Senate Leadership Fund and a former top McConnell aide. "The president is strongly admired in the state. And I think his support does rub off on Senator Strange."

That is why Strange is tethering himself to the president, even as Trump has clashed with many of the mainstream GOP leaders in Washington who back the senator, including McConnell.

"Others attack our president," Strange says in one of his ads. "I'm fighting with him to drain the swamp and repeal Obamacare."

A poll conducted Monday through Wednesday for the Senate Leadership Fund, a McConnell-affiliated PAC planning to spend heavily in the race, showed Moore garnering 45 percent support to Strange's 41 percent, an edge that is not statistically significant. The Voter Consumer Research survey showed a tighter race than the Aug. 15 primary margin. Some public polls have shown Moore ahead with a larger lead.

Some strategists with an eye on the race attribute some of Moore's success to how well-known he is in Republican circles. Moore has not criticized Trump, and he has relentlessly attacked "the swamp" in the same terms as the president. This has made it more challenging for Strange and his allies to go after him, even with the president in their corner.

Moore also is framing himself as a check against McConnell, saying in his fundraising email that "you can count on me to put a stop to Mitch McConnell and his running roughshod over the Senate."

In some regards, he is a candidate in the mold of Trump - which has scrambled the battle lines. Moore even raised doubts last year about Obama's natural-born citizenship, CNN reported this week. For years, Trump questioned Obama's birth before finally admitting last fall that the former president was born in the United States.

Strange also is saddled with the fact that he was appointed by then-Gov. Robert Bentley, who resigned two months later to avoid impeachment amid allegations that he had tried to cover up an extramarital affair. Strange has faced questions on the campaign trail about whether he earned his seat in an effort by Bentley to make the investigation go away. He has responded by pointing to Bentley's resignation as evidence that the integrity of the investigation remained intact despite his departure from the attorney general's office.

Sessions was a key early campaign supporter of Trump, helping drive his success in the South. He has stayed out of the race to replace him.

Strange and Moore have approached Alabama's voters differently, but neither has focused much on large rallies. Moore, a tub-thumbing retail campaigner, has stopped by churches and conservative groups to deliver a stump speech that often ends with a rousing poem about the Declaration of Independence.

The affable Strange, a 6-foot-9 former college basketball player known as "Big Luther," has tended more toward drop-ins at restaurants and public events, having quick conversations with voters while his campaign focuses on turnout.

Strange appeared on WACV radio in Montgomery for an interview this week, saying he had begun to lose his voice from heavy campaigning.

"We're not going to get outworked," he said.

The interview ended up largely focusing on his support for the president. On Afghanistan, Strange said, Trump was "listening to the generals." On North Korea, he had shown resolve and scored a win. On the failure of Obamacare repeal, Strange, like the president, blamed Republican senators for botching the vote, not the executive branch's haphazard salesmanship.

"We were really, really let down by John McCain," he said, referring to the senator from Arizona.

Strange even argued that the president was fulfilling multiple campaign promises by threatening a faceoff with the Senate over how to fund a wall along the Mexican border, suggesting that he might redirect funds from "sanctuary cities" or jawbone Mexico during new NAFTA negotiations.

"I have confidence the president will get it back one way or the other," he said.

National Democratic strategists are keeping an eye on the Alabama contest to weigh whether it is worth investing in, particularly if Moore wins the primary.

Doug Jones, the former U.S. attorney who won the Democratic nomination, said in an interview that he would focus on the core issues of "health care, education and jobs" no matter which Republican wins the primary - but that he would run against Strange as a creature of Washington.

"I don't think he's perceived as a leader," said Jones. "He's certainly not perceived as transparent. And the fact that McConnell is investing so much in him makes it problematic for him to change those impressions."

The difficult relationship between McConnell and Trump has played out publicly in recent weeks. On Thursday, Trump slammed McConnell on Twitter for failing to pass a bill to repeal and replace the Affordable Care Act. McConnell has said Trump had "excessive expectations about how quickly things happen in the democratic process."

Also this week, however, McConnell has sought to project some degree of unity with the president. He praised his administration in many regards during a Thursday speech in Kentucky.

A Strange victory in Alabama could help heal some of the wounds. But a defeat might deepen them.